What are the maximum bag space and Pokemon storage? How many upgrades are needed to reach the limits?

In Pokemon Go, bag space and Pokemon storage are limited. First, what are the starting limits?

More importantly, there are upgrades for 50 Bag Space and 50 Pokemon. How many of each of these upgrades these can be purchased?

With all upgrades purchased, what are the resulting limits?

The current maximum is 3000 for Pokémon storage, and 2500 for item storage.

Originally, it was 1000. As others have also, I fully upgraded mine. I can also confirm that the price stayed the the same for every upgrade purchased to the maximum.

Here is a screenshot of my storage at 1000 each, and the message I got after trying to buy another upgrade once the cap was reached:

Is it worth maxing Pokemon storage? It really does come down to this: for most people, this is NOT necessary. It simply fits the way I wanted to play Pokémon GO. I am not interested in having the highest CP Pokémon or battling Gyms for the time being. I simply enjoy playing "my way", I don't see the value of maxing out Pokémon Storage for 99.999% of players.

Updates:

• In June 2017, max capacity for items was increased to 1500.
• In May 2018, max capacity for items was increased to 2000.
• In July 2019, max capacity for Pokemon was increased to 2500.
• In November 2019, max capacity was increased to 3000 for Pokémon and 2500 for items.

Update: This answer is outdated. Please refer to @JustAHuman's updated answer.

The maximum is 1000 for item storage and 1000 for Pokemon storage.

The limit is 1k/1k

Once you hit 1k the store informs you there is no more upgrades for each

I'm maxed on both so this isn't random guessing